ALBERT

Description: Here we present a method to estimate the total number of nodes of a network using locally observed response dynamics. The algorithm has the following advantages: (a) it is data-driven. Therefore it does not require any prior knowledge about the model; (b) it does not need to collect measurements from multiple stimulus; and (c) it is distributed as it uses local information only, without any prior information about the global network. Even if only a single node is measured, the exact network size can be correctly estimated using a single trajectory. The proposed algorithm has been applied to both linear and nonlinear networks in simulation, illustrating the applicability to real-world physical networks.

Description: The real-time monitoring of reductions of economic activity by containment measures and its effect on the transmission of the coronavirus (COVID-19) is a critical unanswered question. We inferred 5,642 weekly activity anomalies from the meteorology-adjusted differences in spaceborne tropospheric NO2 column concentrations after the 2020 COVID-19 outbreak relative to the baseline from 2016 to 2019. Two satellite observations reveal reincreasing economic activity associated with lifting control measures that comes together with accelerating COVID-19 cases before the winter of 2020/2021. Application of the near-real-time satellite NO2 observations produces a much better prediction of the deceleration of COVID-19 cases than applying the Oxford Government Response Tracker, the Public Health and Social Measures, or human mobility data as alternative predictors. A convergent cross-mapping suggests that economic activity reduction inferred from NO2 is a driver of case deceleration in most of the territories. This effect, however, is not linear, while further activity reductions were associated with weaker deceleration. Over the winter of 2020/2021, nearly 1 million daily COVID-19 cases could have been avoided by optimizing the timing and strength of activity reduction relative to a scenario based on the real distribution. Our study shows how satellite observations can provide surrogate data for activity reduction during the COVID-19 pandemic and monitor the effectiveness of containment to the pandemic before vaccines become widely available.